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The nonlinear fractional Klein–Fock–Gordon (KFG) equation represents an advanced theoretical physics and applied mathematical tool that provides a more extraordinary framework for studying fields with complex and non-standard behaviors. Here, we aim to delve into the new wave profiles of this fractional KGF equation. Initially, this system is successfully converted into an ordinary differential equation (ODE) with the help of wave conversion, and the ODE is solved through the unified and unified solver techniques for the first time. In addition, the 3D and 2D plots of these solutions are drawn using a mathematical software package for different parameters with different values. Therefore, some unique waveforms can be found in these solutions. Moreover, stability and multistability analyses are prepared and shown graphically to confirm the converging limitations of appropriate parameters. This work will be practiced more effectively in future research on nonlinear partial differential models.

Predicting mortality in COVID‐19 is one of the most significant and difficult tasks at hand. This study compares time series and machine learning methods, including support vector machines (SVMs) and neural networks (NNs), to forecast the mortality rate in seven countries: the United States, India, Brazil, Russia, France, China, and Bangladesh. Data were gathered between December 31, 2019, when COVID‐19 began, and March 31, 2021. The study used 457 observations with 4 variables: daily confirmed cases, daily deaths, daily mortality rate, and date. To predict the death rate in the seven countries that were chosen, the data were analyzed using time series analysis and machine learning techniques. Models were compared to obtain more accurate mortality predictions. The autoregressive integrated moving average (ARIMA) model with the lowest AIC value for each nation is found through time series analysis. By increasing the hidden layer and applying machine learning techniques, the NN model for each country is chosen, and the optimal model is determined by determining the model with the lowest error value. Additionally, SVM analyzes every country and calculates its R2 and root‐mean‐square error (RMSE). The lowest RMSE value is used to compare all of the time series and machine learning models. According to the comparison table, SVM provides a more accurate model to predict the mortality rate of the seven countries, with the lowest RMSE value. During the study period, mortality rates increased in Brazil and Russia and decreased in the United States, India, France, China, and Bangladesh, according to the comparison value of RMSE in this study. Furthermore, this paper shows that SVM outperforms all other models in terms of performance. According to the author's analysis of the data, SVM is a machine learning technique that can be used to accurately predict mortality in a pandemic scenario. [ABSTRACT FROM AUTHOR]

This manuscript investigates bifurcation, chaos, and stability analysis for a significant model in the research of shallow water waves, known as the second 3D fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) model. The dynamical system for the above-mentioned nonlinear structure is obtained by employing the Galilean transformation to fulfill the research objectives. Subsequent analysis includes planar dynamic systems techniques to investigate bifurcations, chaos, and sensitivities within the model. Our findings reveal diverse features, including quasi-periodic, periodic, and chaotic motion within the governing nonlinear problem. Additionally, diverse soliton structures, like bright solitons, dark solitons, kink waves, and anti-kink waves, are thoroughly explored through visual illustrations. Interestingly, our results highlight the importance of chaos analysis in understanding complex system dynamics, prediction, and stability. Our techniques' efficiency, conciseness, and effectiveness advance our understanding of this model and suggest broader applications for exploring nonlinear systems. In addition to improving our understanding of shallow water nonlinear dynamics, including waveform features, bifurcation analysis, sensitivity, and stability, this study reveals insights into dynamic properties and wave patterns. [ABSTRACT FROM AUTHOR]

In this study, we proposed and analyzed a nonlinear deterministic mathematical model of malaria transmission dynamics. In addition to the previous approaches, we incorporated the class of aware people and other control measures. We established the wellposedness of the model, and the asymptotic behavior of the solutions is rigorously studied depending on the basic reproduction number R0. The model system admits two equilibrium points: disease‐free and disease‐persistent equilibrium points. The analytical result of the model system revealed that the disease‐free equilibrium point is both locally as well as globally asymptotically stable whenever R0 < 1 while the disease‐persistence equilibrium point is globally asymptotically stable whenever R0 > 1. Moreover, the forward bifurcation phenomenon of the model system for R0 = 1 was analyzed by using center manifold theory. A sensitivity analysis of the basic reproduction number was performed to identify parameters that will cause to trigger the transmission of malaria disease and should be targeted by control strategies. Then, the model was extended to the optimal control problem, with the use of three time‐dependent controls, namely, preventive measures(treated bednets and indoor residual spraying), continuous awareness campaigns to susceptible individuals, and treatment for infected individuals. By using Pontryan's maximum principle, necessary conditions for the transmission of malaria disease were derived. Numerical simulations are illustrated by using MATLAB ode45 to validate the theoretical results of the model. The numerical findings of the optimal model suggested that integrated control strategies are better than a sole intervention to eliminate malaria disease. [ABSTRACT FROM AUTHOR]

In this research, the modified extended tanh-function (METF) and the extended Jacobi elliptic function expansion (EJEFE) techniques are used to investigate the generation and detection of soliton structures in the Hirota–Maccari (HM) model. Consequently, we obtain soliton solutions with advanced structures, including singular bright soliton, dark soliton, periodic waves, breather waves, periodic breather waves, and multiple bright and dark breather waves. In addition, a lump-type breather wave is also included in the presented solutions. Stability analysis of the obtained solutions is addressed by employing the Hamiltonian technique. 3D surfaces and 2D visuals of the outcomes are represented with the help of a computer application. These findings contribute to understanding nonlinear wave phenomena with potential applications in optics, fluid dynamics, and plasma physics. [ABSTRACT FROM AUTHOR]